Question

Calculate the mean for samples where

$$\begin{gathered} \mathbf{a}\mathbf{.}\mathbf{}\mathbf{n}\mathbf{}\mathbf{=}\mathbf{}\mathbf{10}\mathbf{,}\mathbf{}\underset{}{\overset{}{\mathbf{\sum }\mathbf{x}\mathbf{=}\mathbf{25}}} \\ \mathbf{b}\mathbf{.}\mathbf{}\mathbf{n}\mathbf{}\mathbf{=}\mathbf{}\mathbf{16}\mathbf{,}\mathbf{}\underset{}{\overset{}{\mathbf{\sum }\mathbf{x}\mathbf{=}\mathbf{400}}} \\ \mathbf{c}\mathbf{.}\mathbf{}\mathbf{n}\mathbf{}\mathbf{=}\mathbf{}\mathbf{45}\mathbf{,}\mathbf{}\underset{}{\overset{}{\mathbf{\sum }\mathbf{x}\mathbf{=}\mathbf{35}}} \\ \mathbf{d}\mathbf{.}\mathbf{}\mathbf{n}\mathbf{}\mathbf{=}\mathbf{}\mathbf{18}\mathbf{,}\mathbf{}\underset{}{\overset{}{\mathbf{\sum }\mathbf{x}\mathbf{=}\mathbf{242}}} \end{gathered}$$

Short answer

1. 8.5
2. 25
3. 0.78
4. 13.4

Step-by-step solution

Explaining the mean

Mean is the indicator of central tendency, and it comprises all the points from every unit that is there in the research study. Mean can be computed by employing the formula:

$$\begin{gathered} \mathbf{Mean}\mathbf{=}\frac{\mathbf{Summation} \mathbf{of} \mathbf{all} \mathbf{the}\mathbf{terms}}{\mathbf{Number} \mathbf{of} \mathbf{terms}} \\ \mathbf{Mean}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{\sum }\mathbf{x}}{\mathbf{n}} \end{gathered}$$

Calculating the mean for samples

When n = 10 and $\sum \mathrm{x}$= 85, the Mean (M₁) will be,

$$\begin{gathered} {\mathbf{M}}_{\mathbf{1}}\mathbf{=}\frac{\mathbf{85}}{\mathbf{10}} \\ {\mathbf{M}}_{\mathbf{1}}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{5} \end{gathered}$$

Therefore, in this case, the mean value is 8.5.

Computing the mean for samples

When n = 400 and $\sum \mathrm{x}$=16, the Mean (M₂) will be,

$$\begin{gathered} {\mathbf{M}}_{\mathbf{2}}\mathbf{=}\frac{\mathbf{400}}{\mathbf{16}} \\ {\mathbf{M}}_{\mathbf{2}}\mathbf{=}\mathbf{25} \end{gathered}$$

Hence, the mean value is 8.5.

Finding the mean for samples

When n = 45 and $\sum \mathrm{x}$=35, the Mean (M₃) will be,

$$\begin{gathered} {\mathbf{M}}_{\mathbf{3}}\mathbf{=}\frac{\mathbf{35}}{\mathbf{45}} \\ {\mathbf{M}}_{\mathbf{3}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{78} \end{gathered}$$

Thus, the mean is 0.78.

Determining the mean for samples

When n = 18 and $\sum \mathrm{x}$=242, the Mean (M₄) will be,

$$\begin{gathered} {\mathbf{M}}_{\mathbf{4}}\mathbf{=}\frac{\mathbf{242}}{\mathbf{18}} \\ {\mathbf{M}}_{\mathbf{4}}\mathbf{=}\mathbf{13}\mathbf{.}\mathbf{4} \end{gathered}$$

The mean, in this case, is 13.4.